Unbounded device-independent quantum key rates from arbitrarily small non-locality

• URL: http://arxiv.org/abs/2310.08635v3
• Date: Fri, 20 Oct 2023 16:26:15 GMT
• Title: Unbounded device-independent quantum key rates from arbitrarily small non-locality
• Authors: M\'at\'e Farkas
• Abstract summary: Device-independent quantum key distribution allows for proving the security of a shared cryptographic key. Recent results show that Bell non-locality is in general not sufficient for standard device-independent quantum key distribution. We show that from certain correlations that exhibit arbitrarily small non-locality, one can still extract device-independent key rates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell non-local in order to prove security, recent results show that Bell non-locality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of non-locality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small non-locality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell non-locality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes.

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